Wind Power Generation - Renewable Energy: Technology, Economics and Environment - page 302

For a rotating (power generating) wind energy converter, inflow velocity v I at
rotor level v Wi,Rot and circumferential speed of the respective cross-section profile
add up vectorially (Fig. 7.5). Angle γ is determined by vector v I and rotor direc-
tion v R . The inflow angle α represents the difference between angle γ and the
angle of the profile δ . If the inflow angle is supposed to be almost the same over
the entire rotor blade, the angle of attack of the profile must increase steadily from
blade tip to hub as the circumferential speed decreases towards the rotation axis
(rotor blade torsion).
Fig. 7.5 additionally illustrates the entire force incident on the rotor blade F R as
the vectorial total of F D and F L . The figure also reveals that the tangential force
F T , effective on the rotor blade, is calculated by means of the difference between
the tangential components of the drag force F D,t and the lift force F L,t .
Coefficients c l and c d of Equation (7.12) and (7.13) are predetermined by the
rotor profile (shape, surface). Furthermore, they depend on the inflow angle α .
The described correlation can also be represented graphically by the so-called
Lilienthal polars (Fig. 7.6, left). The figure also illustrates the isolated polar
(Fig. 7.6, centre). According to this figure, at a certain inflow angle α operation the
combination of both polars serves to determine the lift c l and drag coefficients c d .
Fig 7.6, left and centre, contains a corresponding schematic representation of
these facts.

v I v I v I

v Wi,Rot v Wi,Rot v Wi,Rot

γ γ γ

v R v R v R

F D,a F D,a F D,a

F D,t F D,t F D,t

Direction of rotation Direction of rotation Turn direction Turn direction Turn direction

α α α

F D F D F D

γ γ γ

F L F L F L

F L,a F L,a F L,a

F D,t F D,t F D,t

F R F R F R

F L,t F L,t F L,t

F T F T F T

F L,t F L,t F L,t

Fig. 7.5 Flow conditions and forces of the airfoil lift principle (for an explanation of sym-
bols see text)

If, by contrast, a vaulted profile shape (Fig. 7.6, right) is used instead of a
symmetrical rotor blade profile, lift force F L , and lift coefficient c l, 0 , are already
created for an inflow angle of 0°. Deviating from profile symmetry to increase
flow diversion thus increases the lift effect which shifts the profile polar curve and
increases the lift coefficient.
Lift coefficient c l can, for instance, be calculated according to Equation (7.14)
for a circular arc profile of arch f and length l (Fig. 7.6, right). The lift coefficient